The earth is moving with some initial momentum
perpendicular to the sun. Newton’s first law
states that an object will remain in motion unless
a force acts on the object to change its motion.

In space there is no friction to slow down
the moving earth, so it will keep moving.
If there were no sun, the earth would travel in
a straight line; however, the sun exerts a
force of gravity on the earth that pulls the
earth and keeps it from flying off into space.

If the earth was moving too fast, the
sun’s gravity would not be enough to keep the
earth in orbit, and it would fly off into space.
If the earth was moving too slow, it would
spiral into the sun due the sun’s gravitational
pull. However, if a planet is moving at just
the right velocity, then it can maintain a stable
orbit around the sun and never fly off or
crash into the sun.

Newton showed that a single planet’s orbit
around the sun is stable, and forms an ellipse
with the sun at one of the focus points. This
orbit will continue indefinitely due to the
constant force of gravity of the sun and law of
conservation of momentum.

Using math to calculate a planet’s orbit is
one of the crowning achievements of the
Enlightenment age. However, this calculation only
considers the earth + sun, and ignores the
possible effect of the other planets and the moon,
all of which exhibit a gravitation force on
each other. Adding in the gravitational
forces of all 8 planets into Newton’s equation
becomes impossible to solve exactly. To study the
stability of the complete solar system, scientists
have used Newton’s laws to simulate the planetary
motion on super computers.

For mathematical reasons, the exact
long-time behavior of the planets is
unpredictable, and so scientists have
performed many computer simulations each starting
from a slightly different set of parameters
(typically shifting the position of each planet by
a random amount of about one millimeter), and
tracing the planetary orbits on the computer.
What are the final results of these
calculations? About 99% of the time, the
computer simulations show that the current
solar system is stable for around 8 billion years
from now until the death of the sun. However,
in 1% of the cases, Mercury collides with Venus at
some point before the death of the sun. In some
rare scenarios this could trigger a larger
instability of the solar system and lead to a
Venus-Earth or Earth-Mars collision, but this is
highly unlikely.

For more information check out space.com (
here )
Or from the Paris Observatory (
here )